2,135 research outputs found
Model approximation for batch flow shop scheduling with fixed batch sizes
Batch flow shops model systems that process a variety of job types using a fixed infrastructure. This model has applications in several areas including chemical manufacturing, building construction, and assembly lines. Since the throughput of such systems depends, often strongly, on the sequence in which they produce various products, scheduling these systems becomes a problem with very practical consequences. Nevertheless, optimally scheduling these systems is NP-complete. This paper demonstrates that batch flow shops can be represented as a particular kind of heap model in the max-plus algebra. These models are shown to belong to a special class of linear systems that are globally stable over finite input sequences, indicating that information about past states is forgotten in finite time. This fact motivates a new solution method to the scheduling problem by optimally solving scheduling problems on finite-memory approximations of the original system. Error in solutions for these “t-step” approximations is bounded and monotonically improving with increasing model complexity, eventually becoming zero when the complexity of the approximation reaches the complexity of the original system.United States. Department of Homeland Security. Science and Technology Directorate (Contract HSHQDC-13-C-B0052)United States. Air Force Research Laboratory (Contract FA8750-09-2-0219)ATK Thiokol Inc
A 64mW DNN-based Visual Navigation Engine for Autonomous Nano-Drones
Fully-autonomous miniaturized robots (e.g., drones), with artificial
intelligence (AI) based visual navigation capabilities are extremely
challenging drivers of Internet-of-Things edge intelligence capabilities.
Visual navigation based on AI approaches, such as deep neural networks (DNNs)
are becoming pervasive for standard-size drones, but are considered out of
reach for nanodrones with size of a few cm. In this work, we
present the first (to the best of our knowledge) demonstration of a navigation
engine for autonomous nano-drones capable of closed-loop end-to-end DNN-based
visual navigation. To achieve this goal we developed a complete methodology for
parallel execution of complex DNNs directly on-bard of resource-constrained
milliwatt-scale nodes. Our system is based on GAP8, a novel parallel
ultra-low-power computing platform, and a 27 g commercial, open-source
CrazyFlie 2.0 nano-quadrotor. As part of our general methodology we discuss the
software mapping techniques that enable the state-of-the-art deep convolutional
neural network presented in [1] to be fully executed on-board within a strict 6
fps real-time constraint with no compromise in terms of flight results, while
all processing is done with only 64 mW on average. Our navigation engine is
flexible and can be used to span a wide performance range: at its peak
performance corner it achieves 18 fps while still consuming on average just
3.5% of the power envelope of the deployed nano-aircraft.Comment: 15 pages, 13 figures, 5 tables, 2 listings, accepted for publication
in the IEEE Internet of Things Journal (IEEE IOTJ
Tensor Numerical Methods in Quantum Chemistry: from Hartree-Fock Energy to Excited States
We resume the recent successes of the grid-based tensor numerical methods and
discuss their prospects in real-space electronic structure calculations. These
methods, based on the low-rank representation of the multidimensional functions
and integral operators, led to entirely grid-based tensor-structured 3D
Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core
Hamiltonian and two-electron integrals (TEI) in complexity using
the rank-structured approximation of basis functions, electron densities and
convolution integral operators all represented on 3D
Cartesian grids. The algorithm for calculating TEI tensor in a form of the
Cholesky decomposition is based on multiple factorizations using algebraic 1D
``density fitting`` scheme. The basis functions are not restricted to separable
Gaussians, since the analytical integration is substituted by high-precision
tensor-structured numerical quadratures. The tensor approaches to
post-Hartree-Fock calculations for the MP2 energy correction and for the
Bethe-Salpeter excited states, based on using low-rank factorizations and the
reduced basis method, were recently introduced. Another direction is related to
the recent attempts to develop a tensor-based Hartree-Fock numerical scheme for
finite lattice-structured systems, where one of the numerical challenges is the
summation of electrostatic potentials of a large number of nuclei. The 3D
grid-based tensor method for calculation of a potential sum on a lattice manifests the linear in computational work, ,
instead of the usual scaling by the Ewald-type approaches
Superparticle Models with Tensorial Central Charges
A generalization of the Ferber-Shirafuji formulation of superparticle
mechanics is considered. The generalized model describes the dynamics of a
superparticle in a superspace extended by tensorial central charge coordinates
and commuting twistor-like spinor variables. The D=4 model contains a
continuous real parameter and at a=0 reduces to the SU(2,2|1)
supertwistor Ferber-Shirafuji model, while at a=1 one gets an OSp(1|8)
supertwistor model of ref. [1] (hep-th/9811022) which describes BPS states with
all but one unbroken target space supersymmetries. When 0<a<1 the model admits
an OSp(2|8) supertwistor description, and when a>1 the supertwistor group
becomes OSp(1,1|8). We quantize the model and find that its quantum spectrum
consists of massless states of an arbitrary (half)integer helicity. The
independent discrete central charge coordinate describes the helicity spectrum.
We also outline the generalization of the a=1 model to higher space-time
dimensions and demonstrate that in D=3,4,6 and 10, where the quantum states are
massless, the extra degrees of freedom (with respect to those of the standard
superparticle) parametrize compact manifolds. These compact manifolds can be
associated with higher-dimensional helicity states. In particular, in D=10 the
additional ``helicity'' manifold is isomorphic to the seven-sphere.Comment: 32 pages, LATEX, no figure
Computational barriers in minimax submatrix detection
This paper studies the minimax detection of a small submatrix of elevated
mean in a large matrix contaminated by additive Gaussian noise. To investigate
the tradeoff between statistical performance and computational cost from a
complexity-theoretic perspective, we consider a sequence of discretized models
which are asymptotically equivalent to the Gaussian model. Under the hypothesis
that the planted clique detection problem cannot be solved in randomized
polynomial time when the clique size is of smaller order than the square root
of the graph size, the following phase transition phenomenon is established:
when the size of the large matrix , if the submatrix size
for any , computational complexity
constraints can incur a severe penalty on the statistical performance in the
sense that any randomized polynomial-time test is minimax suboptimal by a
polynomial factor in ; if for any
, minimax optimal detection can be attained within
constant factors in linear time. Using Schatten norm loss as a representative
example, we show that the hardness of attaining the minimax estimation rate can
crucially depend on the loss function. Implications on the hardness of support
recovery are also obtained.Comment: Published at http://dx.doi.org/10.1214/14-AOS1300 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
We review the black hole entropy calculation in the framework of Loop Quantum
Gravity based on the quasi-local definition of a black hole encoded in the
isolated horizon formalism. We show, by means of the covariant phase space
framework, the appearance in the conserved symplectic structure of a boundary
term corresponding to a Chern-Simons theory on the horizon and present its
quantization both in the U(1) gauge fixed version and in the fully SU(2)
invariant one. We then describe the boundary degrees of freedom counting
techniques developed for an infinite value of the Chern-Simons level case and,
less rigorously, for the case of a finite value. This allows us to perform a
comparison between the U(1) and SU(2) approaches and provide a state of the art
analysis of their common features and different implications for the entropy
calculations. In particular, we comment on different points of view regarding
the nature of the horizon degrees of freedom and the role played by the
Barbero-Immirzi parameter. We conclude by presenting some of the most recent
results concerning possible observational tests for theory
Inflationary observables in loop quantum cosmology
The full set of cosmological observables coming from linear scalar and tensor
perturbations of loop quantum cosmology is computed in the presence of
inverse-volume corrections. Background inflationary solutions are found at
linear order in the quantum corrections; depending on the values of
quantization parameters, they obey an exact or perturbed power-law expansion in
conformal time. The comoving curvature perturbation is shown to be conserved at
large scales, just as in the classical case. Its associated Mukhanov equation
is obtained and solved. Combined with the results for tensor modes, this yields
the scalar and tensor indices, their running, and the tensor-to-scalar ratio,
which are all first order in the quantum correction. The latter could be
sizable in phenomenological scenarios. Contrary to a pure minisuperspace
parametrization, the lattice refinement parametrization is in agreement with
both anomaly cancellation and our results on background solutions and linear
perturbations. The issue of the choice of parametrization is also discussed in
relation with a possible superluminal propagation of perturbative modes, and
conclusions for quantum spacetime structure are drawn.Comment: 41 pages; v2: minor typos corrected, summary of results adde
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